Introduction

Hi team! This is my first true stab at the data. I addressed 4 different hypotheses, each with their own sections. The first hypothesis does not seem to have a ‘positive’ outcome however the last three show some promise. With full intent to bias you, the underdog hypothesis (number 3) is my favorite.

I will step through each of the hypotheses in order, with their corresponding R-code, outputs, and a quick discussion.

At the end, I have a quick mention to the Inter-Rater analysis. I had hoped to find a way to automate an event by event comparison, however the task seems to beating me. I am currently only doing ICC for sheer frequency of touches across each inter-rater match.

Additionally, here is a link to the git-hub repository containing my code and the raw data spreadsheets if you would like to take a look. I may have to give you permission to access them, apologies for the extra step: (https://github.com/paigeliebel/Soccer_Touch.git)

For readability, the code required for cleaning, merging, and fixing typos in the data frames was excluded from this report. You can see the code in the github.

Hypothesis 1: Touch as a Metric for End of Season Success

Core Hypothesis: Pro-social touches between teammates may serve as an indicator for overall team cohesion. Therefore, we propose that teams with a greater frequency of these interactions will secure higher positions in the season’s final standings.

Definitions:

Pro-social touches are defined as all haptic rituals recorded excluding: Tactical Adjustments, Collisions, and Negative Touch

Situations excluded from analysis for this hypothesis: Goals For/Against, Substitutions

library(tidyverse)
library(data.table)
library(broom)
library(janitor)
library(readxl)
library(rmarkdown)
library(readr)
library (dplyr)

Exclude_Touch <- c("TA", "CO", "NEG")
Exclude_Situation <- c("GF", "GA", "SUB") 
#Exclude_Visibility <- c("P")

#Creates data set for core hypothesis analysis
Touches_CoreHyp <- Touches_final %>%
  filter(!(HapticRitual %in% Exclude_Touch)) %>%
  filter(!(Situation %in% Exclude_Situation)) #%>% 
  #filter(!(Visibility %in% Exclude_Visibility))

#Count of frequency of touches per team
Touches_by_team <- Touches_CoreHyp %>%
  mutate(Team = str_trim(as.character(Team))) %>%
  count(Team, name = "TotalTouches")

# Make sure TeamID is padded to match
FinalStandings <- FinalStandings %>%
  mutate(TeamID = str_pad(as.character(TeamID), width = 2, pad = "0"))

#Join touch counts with final standings
Team_Touches_Standings <- FinalStandings %>%
  left_join(Touches_by_team, by = c("TeamID" = "Team")) %>%
  filter(!is.na(TotalTouches))

#Plot with regression line : final rankings to frequency of touch
TouchFreq_vs_FinalStandings <- ggplot(Team_Touches_Standings, aes(x = Rank, y = TotalTouches)) +
  geom_point(size = 3) +
  geom_smooth(method = "lm", se = FALSE, color = "blue", linewidth = 1) +
  scale_x_reverse() +
  labs(
    title = "Final Rank vs Overall Touch Frequency",
    x = "Final Season Rank",
    y = "Total Touches (Filtered)"
  ) +
  theme_minimal()

TouchFreq_vs_FinalStandings_Stats <- cor_result <- cor.test(Team_Touches_Standings$TotalTouches, Team_Touches_Standings$Rank)

Results for Hypothesis 1:

## 
##  Pearson's product-moment correlation
## 
## data:  Team_Touches_Standings$TotalTouches and Team_Touches_Standings$Rank
## t = -0.072115, df = 12, p-value = 0.9437
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.5453701  0.5154585
## sample estimates:
##         cor 
## -0.02081319

As seen in the results above, there does NOT appear to be a strong correlation between total frequency of pro-social touch and overall end of season success. This is counter to the Kraus Basketball paper who concluded more touch leads to more success.

However, I am interested in looking at other factors that could be indicative of touch paired to end of season success. The fact that I excluded goal celebrations is vital. Could we include Goal Celebration touches but control for the number of goals scored?

Perhaps, I can convince one of the masters students to dive into these other hypotheses.

Sub-Hypothesis 1

Hypothesis 1.a: Teams that show less variability across matches throughout a season with regards to their touch will secure higher positions in the season’s final standings.

For the Sub-Hypothesis the touches were scaled for each team based on MAD (mean absolute distance). There was a need to scale touch per team as some teams are ‘touchier’ than others.

########## Within-Team Variability in Touch Frequency ########## 

# Looks at the variability a team has across matches throughout the season

# Count touches per team per game from CoreHyp data frame
Touches_per_game <- Touches_CoreHyp %>%
  group_by(Team, SeasonMatchNumber) %>%
  summarise(TouchCount = n(), .groups = "drop")

# Computing Within-Team Variability
Team_touch_variability <- Touches_per_game %>%
  group_by(Team) %>%
  summarise(
    MeanTouches = mean(TouchCount),
    SDTouches = sd(TouchCount),
    MinTouches = min(TouchCount),
    MaxTouches = max(TouchCount),
    NumGames = n(),
    .groups = "drop"
  )

# Join season rank to each team for ordering in the plot
Touches_per_game_ranked <- Touches_per_game %>%
  mutate(Team = str_pad(as.character(Team), width = 2, pad = "0")) %>%
  left_join(FinalStandings %>% select(TeamID, Rank), by = c("Team" = "TeamID")) %>%
  filter(!is.na(Rank))  # make sure we only include ranked teams

# Visualize 
TouchesPerGame_vs_rank <- ggplot(Touches_per_game_ranked, aes(x = Rank, y = TouchCount, group = Rank)) +
  geom_boxplot(fill = "lightblue", color = "black") +
  scale_x_reverse(breaks = 1:14) +  # clean 1–14 axis
  labs(
    title = "Variation of Within-Team Touch Frequency per Game",
    x = "Team (Ordered by Final Rank)",
    y = "Touches per Game"
  ) +
  theme_minimal()

# Scale touch based on distance from mean (MAD-based z-score)
# How extreme a touch count is compared to team's norm
Touches_scaled <- Touches_per_game %>%
  group_by(Team) %>%
  mutate(
    MedianTouch = median(TouchCount),
    MAD = mad(TouchCount),  # median absolute deviation
    ScaledTouch = (TouchCount - MedianTouch) / MAD
  ) %>%
  ungroup()

# Join Touches_scaled with ranks
Touches_scaled_ranked <- Touches_scaled %>%
  mutate(Team = str_pad(as.character(Team), width = 2, pad = "0")) %>%
  left_join(FinalStandings %>% select(TeamID, Rank), by = c("Team" = "TeamID")) %>%
  filter(!is.na(Rank))

# Plot of MAD
MAD_TouchesPerGame_vs_rank <- ggplot(Touches_scaled_ranked, aes(x = Rank, y = ScaledTouch, group = Rank)) +
  geom_boxplot(fill = "lightblue", color = "black") +
  geom_hline(yintercept = c(-2, 2), linetype = "dashed", color = "red") +
  scale_x_reverse(breaks = 1:14) +  # clean 1–14 axis
  labs(
    title = "Scaled Touch Deviation from Team Median",
    subtitle = "Boxplot of (TouchCount - Median) / MAD per Team",
    x = "Team (Ordered by Final Rank)",
    y = "Scaled Touch Value (MAD Units)"
  ) +
  theme_minimal()

########## Within-Team Variability in Touch Frequency vs Ranking ########## 

# Join variability data to final standings
Variability_vs_Rank <- Team_touch_variability %>%
  mutate(Team = str_pad(as.character(Team), width = 2, pad = "0")) %>%
  left_join(FinalStandings %>% select(TeamID, Rank), by = c("Team" = "TeamID")) %>%
  filter(!is.na(Rank))

# Plot SDTouches vs Rank
Within_Variability_vs_Rank <- ggplot(Variability_vs_Rank, aes(x = Rank, y = SDTouches)) +
  geom_point(size = 3) +
  geom_smooth(method = "lm", se = FALSE, color = "blue", linewidth = 1) +
  scale_x_reverse(breaks = 1:14) +
  labs(
    title = "Team Variability in Touch vs Final Rank",
    x = "Final Season Rank",
    y = "Touch Frequency Variability (SD)"
  ) +
  theme_minimal()

Within_Variability_vs_Rank_Stats <- cor.test(Variability_vs_Rank$SDTouches, Variability_vs_Rank$Rank)

#In regards to within-team variability including MAD scaling

Team_scaled_variability <- Touches_scaled %>%
  group_by(Team) %>%
  summarise(
    SD_ScaledTouch = sd(ScaledTouch),
    NumGames = n(),
    .groups = "drop"
  )

Team_scaled_variability_ranked <- Team_scaled_variability %>%
  mutate(Team = str_pad(as.character(Team), width = 2, pad = "0")) %>%
  left_join(FinalStandings %>% select(TeamID, Rank), by = c("Team" = "TeamID")) %>%
  filter(!is.na(Rank))

Team_scaled_variability_ranked_plot <- ggplot(Team_scaled_variability_ranked, aes(x = Rank, y = SD_ScaledTouch)) +
  geom_point(size = 3) +
  geom_smooth(method = "lm", se = FALSE, color = "red", linewidth = 1) +
  scale_x_reverse(breaks = 1:14) +
  labs(
    title = "Team Variability (SD of Scaled Touch) vs Final Rank",
    x = "Final Season Rank",
    y = "SD of Scaled Touch (MAD units)"
  ) +
  theme_minimal()

ScaledTouch_Variability_vs_Rank_Stats <- cor.test(
  Team_scaled_variability_ranked$SD_ScaledTouch,
  Team_scaled_variability_ranked$Rank
)

Results for Sub-Hypothesis 1

The above graph is showing a breakdown of within-team touch variation per game. Each block is one team, with the most successful team ranked in place 1 on the far right. Each team played 26 games throughout the season. Therefore, each block has 26 data points from which is being built.

The above graph is similar to the previous one, however it scales the touches.

MAD was used instead of SD due to the non-normal nature of the data.

The following formulas were used:

Mean Absolute Deviation (MAD) \[ \text{MAD} = \text{median} \left( \left| X_i - \text{median}(X) \right| \right) \] Scaled Touch \[ \text{ScaledTouch}_i = \frac{ X_i - \text{median}(X) }{ \text{MAD} } \]

Then I looked at the with-in team variation across teams. In other words, does consistency of touch frequencies correlate to end of season standings? I looked at just standard deviation of overall touch, not scaled:

## 
##  Pearson's product-moment correlation
## 
## data:  Variability_vs_Rank$SDTouches and Variability_vs_Rank$Rank
## t = 0.96201, df = 12, p-value = 0.355
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3065156  0.6989310
## sample estimates:
##       cor 
## 0.2675808

Then I took a look at the scaled touch version:

Team_scaled_variability_ranked_plot
## `geom_smooth()` using formula = 'y ~ x'

ScaledTouch_Variability_vs_Rank_Stats
## 
##  Pearson's product-moment correlation
## 
## data:  Team_scaled_variability_ranked$SD_ScaledTouch and Team_scaled_variability_ranked$Rank
## t = 1.5994, df = 12, p-value = 0.1357
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.1432663  0.7769560
## sample estimates:
##       cor 
## 0.4191765

Neither proved to be statistically significant.

Hypothesis 2: Inter-Match Variability

The frequency of pro-social touch across teams may vary due to confounding variables such as team culture or tactics. Therefore, instead of analyzing team to team variations, we suggest that the inter-match variability of pro-social touches within an individual team could be used as an indicator for individual match outcomes. We propose that teams with more pro-social touches within a match than their respective season average are more likely to have a higher goal differential.

Statistically Significant Results. Yay.

Note: Whereas hypothesis 1 looked at outcomes for the whole season, hypothesis 2 is looking at a match level outcome.

Additionally, I ran a Wilcoxon test in fear that the results were not nicely distributed.

# Inter-Match Variability Hypothesis
# For more information on these data frames please look at the README.md file

library(tidyverse)
library(data.table)
library(broom)
library(janitor)
library(readxl)
library(rmarkdown)
library(readr)
library (dplyr)

#Ensure to use the correct dfs. Touches_final and Matches_final are correct. They only include assigned rater data, no repeat matches

#Check to make sure data frames are loaded:
if (!exists("Touches_final") | !exists("Matches_final") | !exists("FinalStandings") | !exists("Touches_CoreHyp")) {
  stop("Touches_final, Matches_final, Touhe_CoreHyp or FinalStandings not loaded. Check Data_Management.R and Core_Hypothesis.R.")
}

############## Inter-Match Variability Hypothesis ############## 

# Basically asking: "When a team is more (or less) touchy than usual, do they score more or less goals than their opponent?"
# Note that this is still using same CoreHyp touches (therefore only prosocial touches and not including GF, GA, Subs etc)

#Clean Match column data for use
Matches_final_cleaned <- Matches_final %>%
  mutate(
    GoalsFor = as.numeric(str_trim(GoalsFor)),
    GoalsAgainst = as.numeric(str_trim(GoalsAgainst))
  )

#Get TeamID into Matches_final
Matches_finalID <- Matches_final_cleaned %>%
  mutate(
    MatchID = str_pad(MatchID, width = 4, pad = "0"),  # in case it was shortened
    TeamID = str_sub(MatchID, 1, 2),                     # preserve leading zeros
    GoalDiff = GoalsFor - GoalsAgainst
  )

# Prosocial touches per team per match
Touches_per_match <- Touches_CoreHyp %>%
  group_by(Team, SeasonMatchNumber) %>%
  summarise(TouchCount = n(), .groups = "drop")

# Average touch per team over the season
Team_season_avg <- Touches_per_match %>%
  group_by(Team) %>%
  summarise(SeasonAvgTouch = mean(TouchCount), .groups = "drop")

# Merge & calculate scaled deviation from average
Touches_scaled_dev <- Touches_per_match %>%
  left_join(Team_season_avg, by = "Team") %>%
  mutate(ScaledAboveAvg = TouchCount - SeasonAvgTouch) # positive = more touchy than average, neg = less touchy than average

# Joins dataframes (goal differetials to the touches scaled)
Touch_GoalDiff_Analysis <- Touches_scaled_dev %>%
  left_join(
    Matches_finalID %>% select(SeasonMatchNumber, TeamID, GoalDiff),
    by = c("SeasonMatchNumber", "Team" = "TeamID")
  )

# Visualize 
Touch_GoalDiff_Analysis_Graph <- ggplot(Touch_GoalDiff_Analysis, aes(x = ScaledAboveAvg, y = GoalDiff)) +
  geom_point(size = 2, alpha = 0.7) +
  geom_smooth(method = "lm", se = FALSE, color = "blue") +
  labs(
    title = "Touch Count Deviation vs Match Goal Differential",
    x = "Touches Above/Below Team Average",
    y = "Goal Differential",
    caption = "Note: Each dot represents one match outcome for a team, therefore 2 dots for each match"
  ) +
  theme_minimal()

# Pearson
Touch_GoalDiff_Analysis_Stats <- cor.test(Touch_GoalDiff_Analysis$ScaledAboveAvg, Touch_GoalDiff_Analysis$GoalDiff)

############## Wilcoxon: Inter-Match Variability Hypothesis ############## 

# Wilcoxon: Perhaps not nicely distributed: “Do teams tend to have higher goal differentials when they are more touchy than their season average?”

# Create AboveAvgTouch flag
Touch_AboveBelow_Analysis <- Touch_GoalDiff_Analysis %>%
  mutate(AboveAvgTouch = ScaledAboveAvg > 0)

# Summary of goal differentials by touch group
Touch_AboveBelow_Analysis %>%
  group_by(AboveAvgTouch) %>%
  summarise(
    n = n(),
    mean_GD = mean(GoalDiff, na.rm = TRUE),
    median_GD = median(GoalDiff, na.rm = TRUE),
    sd_GD = sd(GoalDiff, na.rm = TRUE)
  )
## # A tibble: 2 × 5
##   AboveAvgTouch     n mean_GD median_GD sd_GD
##   <lgl>         <int>   <dbl>     <dbl> <dbl>
## 1 FALSE           202  -0.444        -1  1.52
## 2 TRUE            162   0.581         1  1.69
# Wilcoxon rank-sum test
Wilcox_Test <- wilcox.test(GoalDiff ~ AboveAvgTouch, data = Touch_AboveBelow_Analysis)

# Visualize Wilcoxon
Wilcox_Test_Graph <- ggplot(Touch_AboveBelow_Analysis, aes(x = AboveAvgTouch, y = GoalDiff)) +
  geom_boxplot(fill = "lightblue") +
  scale_x_discrete(labels = c("FALSE" = "Below Avg Touch", "TRUE" = "Above Avg Touch")) +
  labs(
    title = "Goal Differential by Above/Below Avg Touch",
    x = "Above Team's Avg Touch?",
    y = "Goal Differential"
  ) +
  theme_minimal()

Results for Hypothesis 2:

## 
##  Pearson's product-moment correlation
## 
## data:  Touch_GoalDiff_Analysis$ScaledAboveAvg and Touch_GoalDiff_Analysis$GoalDiff
## t = 5.6914, df = 312, p-value = 2.906e-08
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2028881 0.4036665
## sample estimates:
##      cor 
## 0.306685
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  GoalDiff by AboveAvgTouch
## W = 7714, p-value = 1.949e-08
## alternative hypothesis: true location shift is not equal to 0

Hypothesis 3: Underdog Hypothesis

Teams with greater frequencies of pro-social touch when competing against higher ranked teams will secure a better goal differential than teams with fewer touch instances facing an opponent of the same spread in rankings.

Statistically Significant Result! Yay.

Definition of spread: Spread in rankings is defined as the difference in current standings the teams have between each other. Therefore, the 1st ranked team competing against the 7th ranked team has the same spread as the 7th ranked team playing against the 14th ranked team. This could expose a team’s cohesion by how they react when facing adversity.

Touch is scaled again using MAD.

I used both an ANOVA (which described nothing of interest) and a GAM model (which I love).

Note: First 13 matches of season are excluded. Not all teams play the first weekend of the season. Therefore, the current standings only have a ‘comprehensive picture’ going into the 3rd weekend. In other words, after match 13, at least every team has completed 1 game.

Additionally, for the categorical analysis I arbitrarily determined that a spread between 0-7 was a “mild underdog” or a “mild favorite. A spread greater than 7 was considered”major”. This is simply because there are 14 teams in the league and a spread of 7 would place a team on teh other half of the table.

# Underdog Hypothesis

library(tidyverse)
library(data.table)
library(broom)
library(janitor)
library(readxl)
library(rmarkdown)
library(readr)
library (dplyr)
library(plotly)
library(mgcv)
library(ggplot2)
library(forcats)

#Ensure to use the correct dfs. Touches_final and Matches_final are correct. They only include assigned rater data, no repeat matches

#Check to make sure data frames are loaded:

if (!exists("Touches_final") | !exists("Touches_scaled") | !exists("Matches_finalID") | !exists("FinalStandings") | !exists("Touches_CoreHyp")) {
  stop("Touches_final, Matches_final, Touhe_CoreHyp or FinalStandings not loaded. Check Data_Management.R and Core_Hypothesis.R.")
}

############################ Underdog Hypothesis ############################

# Clean Match column data for use
Matches_final_cleaned_CurrentStandings <- Matches_final %>%
  mutate(
    GoalsFor = as.numeric(str_trim(GoalsFor)),
    GoalsAgainst = as.numeric(str_trim(GoalsAgainst)),
    CurrentStanding = as.numeric(str_trim(CurrentStanding)),
    MatchID = str_pad(MatchID, width = 4, pad = "0"),  # ensure 4-digit MatchID
    TeamID = str_sub(MatchID, 1, 2),                   # extract TeamID from MatchID
    SeasonMatchNumber = as.numeric(SeasonMatchNumber)  # ensure it can be compared numerically
  ) %>%
  filter(SeasonMatchNumber > 13)  # exclude first 13 matches

# Get the spread into the info for each team
Matches_final_Spread <- Matches_final_cleaned_CurrentStandings %>%
  rename_with(~ paste0(.x, "_self")) %>% #renames every column so that you know which row refers to the self team of analysis
  inner_join(
    Matches_final_cleaned_CurrentStandings,
    by = c("SeasonMatchNumber_self" = "SeasonMatchNumber") # joins data frame to itself, matching each game via seasonmatchnumber (_self is of interst) (wihtout is opponent)
  ) %>%
  filter(TeamID_self != TeamID) %>%  # Make sure we’re not joining a row to itself
  mutate(
    GoalDiff = GoalsFor_self - GoalsAgainst_self,
    Spread = CurrentStanding - CurrentStanding_self  # positive = better ranked than opponent, negative = underdog
  ) %>%
  select(
    SeasonMatchNumber = SeasonMatchNumber_self,
    MatchID = MatchID_self,
    TeamID = TeamID_self,
    GoalDiff,
    Spread,
    CurrentStanding = CurrentStanding_self,
    OpponentTeamID = TeamID,
    OpponentStanding = CurrentStanding
  )

#Correcting data types
Touches_scaled_numeric <- Touches_scaled %>%
  mutate(
    SeasonMatchNumber = as.numeric(SeasonMatchNumber),
    Team = as.character(Team)  # just to ensure consistency
  )

# Data frame creation for Underdog analysis
Underdog_Analysis <- Matches_final_Spread %>%
  left_join(
    Touches_scaled_numeric,
    by = c("SeasonMatchNumber", "TeamID" = "Team")
  )

############################ Observed Data Table Summary | Underdog Hypothesis ############################

spread_cutoff <- 7 #arbitrary spread number: I like 7 because it separates the table in half (1st rank team playing against bottom half of table)

# Categorize real match data into underdog/favored + touch level
Underdog_Observed_Summary <- Underdog_Analysis %>%
  filter(!is.na(GoalDiff) & !is.na(ScaledTouch) & !is.na(Spread)) %>%  # ensure clean data
  mutate(
    SpreadGroup = case_when(
      Spread <= -spread_cutoff ~ "Major Underdog",
      Spread > -spread_cutoff & Spread < 0 ~ "Mild Underdog",
      Spread == 0 ~ "Even",
      Spread > 0 & Spread < spread_cutoff ~ "Mild Favorite",
      Spread >= spread_cutoff ~ "Major Favorite"
    ),
    TouchGroup = case_when(
      ScaledTouch >= 1 ~ "High Touch",
      ScaledTouch <= -1 ~ "Low Touch",
      TRUE ~ "Average Touch"
    )
  ) %>%
  group_by(SpreadGroup, TouchGroup) %>%
  summarise(
    MeanObservedGD = mean(GoalDiff, na.rm = TRUE),
    n = n(),
    .groups = "drop"
  ) %>%
  arrange(SpreadGroup, TouchGroup)

#Bar chart for this data: I think easier to understand than the cool looking 3D chart generated below.
# Set factor levels for order
spread_levels <- c("Major Underdog", "Mild Underdog", "Even", "Mild Favorite", "Major Favorite")
touch_levels <- c("Low Touch", "Average Touch", "High Touch")

# Make sure SpreadGroup and TouchGroup are ordered
Underdog_Observed_Summary <- Underdog_Observed_Summary %>%
  mutate(
    SpreadGroup = factor(SpreadGroup, levels = spread_levels),
    TouchGroup = factor(TouchGroup, levels = touch_levels)
  )

# Plot observed data
Barchart_Categorical_Data <- ggplot(Underdog_Observed_Summary, aes(x = SpreadGroup, y = MeanObservedGD, fill = TouchGroup)) +
  geom_col(position = position_dodge(width = 0.8), width = 0.7) +
  geom_text(
    aes(label = paste0("n=", n)),
    position = position_dodge(width = 0.8),
    vjust = ifelse(Underdog_Observed_Summary$MeanObservedGD >= 0, -0.5, 1.2),
    size = 3.5
  ) +
  scale_fill_brewer(palette = "Blues") +
  labs(
    title = "Observed Goal Differential by Underdog/Favorite Status and Touch Level",
    x = "Underdog/Favorite Status (Spread Group)",
    y = "Mean Goal Differential",
    fill = "Touch Level"
  ) +
  theme_minimal() +
  theme(legend.position = "bottom")

# Statistically compare goal differentials across spreadgroup and touchgroup
# Via a two-way ANOVa 
# Make sure grouping variables are factors
Underdog_Observed_ANOVA <- Underdog_Analysis %>%
  filter(!is.na(GoalDiff) & !is.na(ScaledTouch) & !is.na(Spread)) %>%
  mutate(
    SpreadGroup = case_when(
      Spread <= -spread_cutoff ~ "Major Underdog",
      Spread > -spread_cutoff & Spread < 0 ~ "Mild Underdog",
      Spread == 0 ~ "Even",
      Spread > 0 & Spread < spread_cutoff ~ "Mild Favorite",
      Spread >= spread_cutoff ~ "Major Favorite"
    ),
    TouchGroup = case_when(
      ScaledTouch >= 1 ~ "High Touch",
      ScaledTouch <= -1 ~ "Low Touch",
      TRUE ~ "Average Touch"
    ),
    SpreadGroup = factor(SpreadGroup, levels = spread_levels),
    TouchGroup = factor(TouchGroup, levels = touch_levels)
  )

# Run Two-Way ANOVA
anova_result <- aov(GoalDiff ~ SpreadGroup * TouchGroup, data = Underdog_Observed_ANOVA)
ANOVASUM <- summary(anova_result)
TukeryAnova <- TukeyHSD(anova_result)

#Summary Table of Means and SDs per Group
Underdog_Observed_ANOVA %>%
  group_by(SpreadGroup, TouchGroup) %>%
  summarise(
    Mean_GD = mean(GoalDiff, na.rm = TRUE),
    SD_GD = sd(GoalDiff, na.rm = TRUE),
    n = n(),
    .groups = "drop"
  ) %>%
  arrange(SpreadGroup, TouchGroup)
## # A tibble: 12 × 5
##    SpreadGroup    TouchGroup    Mean_GD SD_GD     n
##    <fct>          <fct>           <dbl> <dbl> <int>
##  1 Major Underdog Low Touch      -1.88   1.89     8
##  2 Major Underdog Average Touch  -1.08   1.41    25
##  3 Major Underdog High Touch     -0.6    1.67     5
##  4 Mild Underdog  Low Touch      -1.35   1.06    17
##  5 Mild Underdog  Average Touch  -0.365  1.52    63
##  6 Mild Underdog  High Touch      0.481  1.53    27
##  7 Mild Favorite  Low Touch      -0.714  1.70     7
##  8 Mild Favorite  Average Touch   0.266  1.51    79
##  9 Mild Favorite  High Touch      0.810  1.57    21
## 10 Major Favorite Low Touch       1.25   1.71     4
## 11 Major Favorite Average Touch   1.2    1.61    30
## 12 Major Favorite High Touch      1      1.41     4
#ANOVA categorically dos not say that spread AND touch together affects goal differential
#It does say that underdogs are more likely to lose (duh) and that more touch is better (duh)
#Look at GAM Model to see other stuff, there it creates a a relationship between the three values

############################ GAM Model | Underdog Hypothesis ############################

#This is asking: If a team is more/less touchy than usual, and they are underdog/overdog, how does this impact the goal differenetial?

# Fit GAM model to allow for nonlinear effects

# Changing k = 15 creates completely flattens slope
gam_model <- gam(
  GoalDiff ~ s(Spread, ScaledTouch, k = 100, bs = "tp"),  # increase k for smoother fit
  data = Underdog_Analysis
)

# Create grid for predictions
spread_seq <- seq(min(Underdog_Analysis$Spread, na.rm = TRUE),
                  max(Underdog_Analysis$Spread, na.rm = TRUE), length.out = 50)
touch_seq <- seq(min(Underdog_Analysis$ScaledTouch, na.rm = TRUE),
                 max(Underdog_Analysis$ScaledTouch, na.rm = TRUE), length.out = 50)

grid <- expand.grid(Spread = spread_seq, ScaledTouch = touch_seq)
grid$GoalDiff <- predict(gam_model, newdata = grid)

# Convert to matrix for surface
z_matrix <- matrix(grid$GoalDiff, nrow = length(spread_seq), ncol = length(touch_seq))

# 3D Plot: See below in next R chunk
#Note: Each dot represents one match outcome for a team, therefore 2 dots for each match
# plot_ly() %>%
#   add_surface(
#     x = ~spread_seq,
#     y = ~touch_seq,
#     z = ~z_matrix,
#     colorscale = list(
#       c(0, "red"),  # red for losses
#       c(1, "green")   # green for wins
#     ),
#     cmin = min(Underdog_Analysis$GoalDiff, na.rm = TRUE),
#     cmax = max(Underdog_Analysis$GoalDiff, na.rm = TRUE),
#     opacity = 0.7,
#     showscale = TRUE
#   ) %>%
#   add_markers(
#     data = Underdog_Analysis,
#     x = ~Spread,
#     y = ~ScaledTouch,
#     z = ~GoalDiff,
#     marker = list(
#       size = 3,
#       color = ~GoalDiff,
#       colorscale = list(c(0, "#ff0000"), c(1, "#00ff00")),  # flipped: red = low, green = high
#       cmin = min(Underdog_Analysis$GoalDiff, na.rm = TRUE),
#       cmax = max(Underdog_Analysis$GoalDiff, na.rm = TRUE)
#     ),
#     name = "Observed"
#   ) %>%
#   layout(
#     title = "Underdog Hypothesis: Spread x Touch Deviation x Goal Differential",
#     scene = list(
#       xaxis = list(title = "Spread (Opponent Rank - Team Rank)"),
#       yaxis = list(title = "Scaled Touch Deviation"),
#       zaxis = list(title = "Goal Differential")
#     )
#   )


############################ GAM Model CATEGORICAL Table Summary (Interpretation of GAM) | Underdog Hypothesis ############################

# Evaluates how a team's goal differential is predicated by a model across a spectrum of two predictors:
# Predictor One = Ranking Spread
# Predictor Two = Scaled Touch Deviation (how much more or less physical touch a team used compared to their norm)

# Backpedals to the observed table CATEGORICAL idea. 

# Define a grid of Spread and ScaledTouch values
# Create a sequence of 100 evenly spaced values from smallest to largest spread
spread_vals <- seq(min(Underdog_Analysis$Spread, na.rm = TRUE),
                   max(Underdog_Analysis$Spread, na.rm = TRUE),
                   length.out = 100)

# Create a sequence of 100 evenly spaced values from smallest to largest touch
touch_vals <- seq(min(Underdog_Analysis$ScaledTouch, na.rm = TRUE),
                  max(Underdog_Analysis$ScaledTouch, na.rm = TRUE),
                  length.out = 100)

# Create a ten thousand row data frame by combining all hundred by hundred values above
grid <- expand.grid(Spread = spread_vals, ScaledTouch = touch_vals)

# Predict GoalDiff across the grid on each fake game (ten thousand of them)
grid$PredictedGoalDiff <- predict(gam_model, newdata = grid)

#Note choice of 7 as the cutoff is somewhat arbitrary
grid_summary <- grid %>%
  mutate(
    SpreadGroup = case_when(
      Spread <= -spread_cutoff ~ "Major Underdog",
      Spread > -spread_cutoff & Spread < 0 ~ "Mild Underdog",
      Spread == 0 ~ "Even",
      Spread > 0 & Spread < spread_cutoff ~ "Mild Favorite",
      Spread >= spread_cutoff ~ "Major Favorite"
    ),
    TouchGroup = case_when(
      ScaledTouch >= 1 ~ "High Touch",
      ScaledTouch <= -1 ~ "Low Touch",
      TRUE ~ "Average Touch"
    )
  ) %>%
  group_by(SpreadGroup, TouchGroup) %>%
  summarise(
    MeanPredGD = mean(PredictedGoalDiff, na.rm = TRUE),
    .groups = "drop"
  ) %>%
  arrange(SpreadGroup, TouchGroup)

#Bar graph to see the GAM model major/mild underdogs versus tables
# Set same factor levels for consistency
grid_summary <- grid_summary %>%
  mutate(
    SpreadGroup = factor(SpreadGroup, levels = spread_levels),
    TouchGroup = factor(TouchGroup, levels = touch_levels)
  )

# Plot GAM model data
GAM_Model_Data_Plot <- ggplot(grid_summary, aes(x = SpreadGroup, y = MeanPredGD, fill = TouchGroup)) +
  geom_col(position = position_dodge(width = 0.8), width = 0.7) +
  scale_fill_brewer(palette = "Blues") +
  labs(
    title = "GAM Model Predicted Goal Differential by Underdog/Favorite Status and Touch Level",
    x = "Underdog/Favorite Status (Spread Group)",
    y = "Predicted Goal Differential",
    fill = "Touch Level"
  ) +
  theme_minimal() +
  theme(legend.position = "bottom")

#Output for Hypothesis 3:

Hypothesis 4: Social Network and Reciprocity

Hyp 4a had a statistically significant result. Hyp 4b did not.

Hypothesis 4.a: We propose that a higher ratio of reciprocal to non-reciprocal touches is indicative of better team cohesion and therefore correlates to a higher finish in the final season standings.

Note: In addition to the situations mentioned previously, Injury Touches were excluded from the reciprocal ratio analysis as they are almost solely non-reciprocal. The injured party rarely touches back as they are in pain on the ground.

Hypothesis 4.b: We propose that teams with a more even distribution of prosocial touch events across players, both giving and receiving, will finish higher in the final season standings.

# Social Network Strength Hypothesis
# For more information on these data frames please look at the README.md file

library(tidyverse)
library(data.table)
library(broom)
library(janitor)
library(readxl)
library(rmarkdown)
library(readr)
library (dplyr)
library(plotly)
library(mgcv)
library(ggplot2)
library(forcats)
library(ggridges)
library(DescTools)


#Ensure to use the correct dfs. Touches_final and Matches_final are correct. They only include assigned rater data, no repeat matches

#Check to make sure data frames are loaded:
if (!exists("Touches_final") | !exists("Touches_scaled") | !exists("Matches_finalID") | !exists("FinalStandings") | !exists("Touches_CoreHyp")) {
  stop("Touches_final, Matches_final, Touhe_CoreHyp or FinalStandings not loaded. Check Data_Management.R and Core_Hypothesis.R.")
}

############################ Social Network Strength ############################

#Clean data to grab what we need: reciprocity, toucher numbers, touchee numbers
#Group event also count towards reciprocal, so long as it is not GF, SUB etc 

Touches_Reciprocal <- Touches_final %>% 
  mutate(
    Team = as.character(Team),
    Reciprocity = str_trim(Reciprocal) #cleans up white spaces in case
  )

FinalStandings <- FinalStandings %>%
  mutate(TeamID = as.character(TeamID)) %>%  # <--- force character
  mutate(TeamID = str_pad(TeamID, width = 2, pad = "0"))

############################ Reciprocal/Non-Reciprocal | Social Network Strength ############################

#Reciprocal vs non-reciprocal touch | simple final standings to ratio of reciprocal/non-reciprocal

# Count touches by team and reciprocity type
Reciprocity_by_Team <- Touches_Reciprocal %>%
  filter(!is.na(Reciprocity)) %>%
  mutate(
    ReciprocityType = case_when(
      Reciprocity %in% c("Y", "G") ~ "Reciprocal", #Reciprocal includes group events
      Reciprocity == "N" ~ "NonReciprocal",
      TRUE ~ NA_character_
    )
  ) %>%
  filter(!is.na(ReciprocityType)) %>%
  group_by(Team, ReciprocityType) %>%
  summarise(TouchCount = n(), .groups = "drop") %>%
  pivot_wider(names_from = ReciprocityType, values_from = TouchCount, values_fill = 0) %>%
  mutate(
    Reciprocal_To_NonRecip_Ratio = Reciprocal / NonReciprocal,
    DataFlag = if_else(Reciprocal + NonReciprocal == 0, "No Touch Data", "Data Available")
  )

#Join with Final Standings
Reciprocal_vs_Rank <- FinalStandings %>%
  mutate(TeamID = str_pad(as.character(TeamID), width = 2, pad = "0")) %>%
  left_join(Reciprocity_by_Team, by = c("TeamID" = "Team"))

#Plot
Reciprocal_Ratio_Graph <- ggplot(Reciprocal_vs_Rank, aes(x = Rank, y = Reciprocal_To_NonRecip_Ratio)) +
  geom_point(size = 3, color = "steelblue") +  # all teams shown in one color
  geom_smooth(
    data = filter(Reciprocal_vs_Rank, !is.na(Reciprocal_To_NonRecip_Ratio)),
    aes(x = Rank, y = Reciprocal_To_NonRecip_Ratio),
    method = "lm", se = FALSE, color = "black"
  ) +
  scale_x_reverse(breaks = 1:max(Reciprocal_vs_Rank$Rank)) +
  labs(
    title = "Reciprocal Touch Ratio vs Final Season Rank per Team",
    subtitle = "Higher ratios may reflect stronger intra-team cohesion",
    caption = "Note: Each dot represents one team",
    x = "Team Final Season Rank",
    y = "Team Touch Ratio (Reciprocal : Non-Reciprocal)",
  ) +
  theme_minimal()

#Stats Sum
reciprocal_lm <- lm(Rank ~ Reciprocal_To_NonRecip_Ratio, data = Reciprocal_vs_Rank)

summary_reciprocal_lm <- summary(reciprocal_lm)

#Creates Dataframe that Flags values that don't match with requirements of strings, jersey numbers, G, SU, ??
#Cleans common typos (which were many)
Touches_players_flagged <- Touches_final %>%
  mutate(
    ToucherNumber = as.character(ToucherNumber),
    ToucheeNumber = as.character(ToucheeNumber),
    PlayersInvolved = as.character(PlayersInvolved),
    PlayersInvolved = PlayersInvolved %>%
      str_replace_all("\\.\\s+", ",") %>%           # fix "10. 12" → "10,12"
      str_remove_all("[\"'`:;.`]") %>%              # Remove unwanted punctuation
      str_replace_all("\\s*,\\s*", ",") %>%         # Normalize commas and spacing
      str_replace_all("\\s+", "") %>%               # Remove stray spaces
      str_replace_all("(?<=\\d{2})(?=\\d{2}$)", ",") %>%       # Insert comma in "1210" → "12,10"
      str_replace(",+$", "") %>%                    # Remove trailing commas
      str_trim(),                                   # Clean up leading/trailing space 
    
    
    # Valid if it's a number, "G", "SU", or "??"
    ToucherNumber_Valid = str_detect(ToucherNumber, "^\\d{1,2}$|^G$|^SU$|^\\?\\?$"),
    ToucheeNumber_Valid = str_detect(ToucheeNumber, "^\\d{1,2}$|^G$|^SU$|^\\?\\?$"),
    
    # Valid PlayersInvolved: at least two elements (numbers or ?? or SU), comma-separated
    PlayersInvolved_List = str_split(PlayersInvolved, ",\\s*"),
    PlayersInvolved_Valid = map_lgl(PlayersInvolved_List, function(players) {
      cleaned <- str_trim(players)
      all_valid <- all(str_detect(cleaned, "^\\d+$|^\\?\\?$|^SU$"))
      has_multiple <- length(cleaned) >= 2
      all_valid && has_multiple
    })
  )

#Splits "12,04,09" back into "12, 04, 09"
Touches_players_flagged <- Touches_players_flagged %>%
  mutate(PlayersInvolved = str_split(PlayersInvolved, ","))

#Ignore those flagged values for now (fix them before final paper)
Touches_players_final <- Touches_players_flagged %>%
  filter(
    ToucherNumber_Valid,
    ToucheeNumber_Valid,
    PlayersInvolved_Valid
  )

############################ Player Concentration | Social Network Strength ############################

# Count number of times each player was the Toucher within each team
toucher_counts <- Touches_players_final %>%
  filter(!is.na(ToucherNumber) & ToucherNumber != "G") %>%
  group_by(Team, ToucherNumber) %>%
  summarise(TouchCount = n(), .groups = "drop")

Toucher_Plot <- ggplot(toucher_counts, aes(x = ToucherNumber, y = TouchCount)) +
  geom_col(fill = "steelblue") +
  facet_wrap(~ Team, scales = "free_x") +
  labs(
    title = "Toucher Frequency by Player Jersey Number",
    x = "Player (ToucherNumber)",
    y = "Number of Touches"
  ) +
  theme_minimal() +
  theme(
    axis.text.x = element_text(angle = 90, vjust = 0.5),
    strip.text = element_text(face = "bold")
  )

#########Histograms for Touchee by team (creates 14 histograms for team by team analysis)

# Count number of times each player was the Touchee within each team
touchee_counts <- Touches_players_final %>%
  filter(!is.na(ToucheeNumber) & ToucheeNumber != "G") %>%
  group_by(Team, ToucheeNumber) %>%
  summarise(TouchCount = n(), .groups = "drop")

Touchee_Plot <- ggplot(touchee_counts, aes(x = ToucheeNumber, y = TouchCount)) +
  geom_col(fill = "steelblue") +
  facet_wrap(~ Team, scales = "free_x") +
  labs(
    title = "Touchee Frequency by Player Jersey Number",
    x = "Player (ToucheeNumber)",
    y = "Number of Touches"
  ) +
  theme_minimal() +
  theme(
    axis.text.x = element_text(angle = 90, vjust = 0.5),
    strip.text = element_text(face = "bold")
  )

#########Histograms for players involved in any touch event, as toucher, touchee or group (creates 14 histograms for team by team analysis)

# Properly split and unnest
player_counts <- Touches_players_final %>%
  select(Team, PlayersInvolved) %>%
  separate_rows(PlayersInvolved, sep = ",\\s*") %>%
  mutate(PlayersInvolved = str_trim(PlayersInvolved)) %>%
  filter(PlayersInvolved != "") %>%
  group_by(Team, PlayersInvolved) %>%
  summarise(TouchCount = n(), .groups = "drop") %>%
  arrange(Team, desc(TouchCount))

AnyTouchPlot <- ggplot(player_counts, aes(x = fct_reorder(PlayersInvolved, -TouchCount), y = TouchCount)) +
  geom_col(fill = "steelblue") +
  facet_wrap(~ Team, scales = "free_x") +
  labs(
    title = "Player Touch Involvement (PlayersInvolved Column)",
    subtitle = "Each bar shows one player's total involvement across the season",
    x = "Player Jersey / Code",
    y = "Touch Count"
  ) +
  theme_minimal() +
  theme(
    axis.text.x = element_text(angle = 90, vjust = 0.5, size = 8),
    strip.text = element_text(face = "bold")
  )


#########Histograms for players involved in group events by team (creates 14 histograms for team by team analysis)

#Filters for just rows that contain the "G"
group_touches <- Touches_players_final %>%
  filter(ToucherNumber == "G")

player_counts_groupsanalysis <- group_touches %>%
  select(Team, PlayersInvolved, ToucherNumber) %>%
  separate_rows(PlayersInvolved, sep = ",\\s*") %>%
  mutate(PlayersInvolved = str_trim(PlayersInvolved)) %>%
  filter(PlayersInvolved != "") %>%
  group_by(Team, PlayersInvolved) %>%
  summarise(TouchCount = n(), .groups = "drop") %>%
  arrange(Team, desc(TouchCount))

#Plots
GroupTouch_Plot <- ggplot(player_counts_groupsanalysis, aes(x = PlayersInvolved, y = TouchCount)) +
  geom_col(fill = "steelblue") +
  facet_wrap(~ Team, scales = "free_x") +
  labs(
    title = "Player Involvement in Group Events (Touches_final)",
    subtitle = "Each bar shows a player's total involvement in group touches",
    x = "Player Jersey",
    y = "Group Touch Count"
  ) +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1))

#########Ridge plot that shows touchiest players stacked on top of each other by team (one plot for all 14 teams)

# Build long-format player count data (from cleaned PlayersInvolved)
player_ridgeplot_counts <- Touches_players_final %>%
  select(Team, PlayersInvolved) %>%
  separate_rows(PlayersInvolved, sep = ",\\s*") %>%
  mutate(PlayersInvolved = str_trim(PlayersInvolved)) %>%
  filter(PlayersInvolved != "") %>%
  group_by(Team, PlayersInvolved) %>%
  summarise(TouchCount = n(), .groups = "drop")

# Assign within-team ranks (1 = most touchy)
player_ridgeplot_counts <- player_ridgeplot_counts %>%
  group_by(Team) %>%
  arrange(desc(TouchCount)) %>%
  mutate(
    TouchiestRank = row_number()  # Numeric: 1 = most touchy
  ) %>%
  ungroup()

# Calculate standard deviation of TouchCount per team
team_SD <- player_ridgeplot_counts %>%
  group_by(Team) %>%
  summarise(TouchSD = sd(TouchCount), .groups = "drop")

# Step 2: Reorder Team factor based on flatness (ascending)
player_ridgeplot_counts <- player_ridgeplot_counts %>%
  left_join(team_SD, by = "Team") %>%
  mutate(Team = fct_reorder(Team, TouchSD, .desc = FALSE))  # flattest first

# Plot ridge plot using numeric ranks
StackedByTouchiest_Plot <- ggplot(player_ridgeplot_counts, aes(x = TouchiestRank, y = fct_rev(Team), height = TouchCount, group = Team)) +
  geom_ridgeline(stat = "identity", fill = "steelblue", color = "white", alpha = 0.8, scale = 0.9) +
  scale_x_continuous(breaks = 1:50, expand = c(0.01, 0)) +
  labs(
    title = "Player Touch Involvement Ridge Plot by Team",
    subtitle = "Teams ordered front-to-back from flattest to most peaked touch distributions",
    x = "Player Touch Rank within Team (1 = Most Involved)",
    y = "Team"
  ) +
  theme_minimal() +
  theme(
    panel.grid.major.y = element_blank(),
    axis.text.y = element_text(size = 8),
    plot.title = element_text(face = "bold")
  )

#Unstacked Ridge plot
Unstacked_RidgePlot_TouchiestPlayers <- ggplot(player_ridgeplot_counts, aes(x = TouchiestRank, y = Team, height = TouchCount, group = Team)) +
  geom_density_ridges(stat = "identity", scale = 1.5, fill = "steelblue", alpha = 0.7) +
  labs(
    title = "Distribution of Player Touch Involvement by Team",
    subtitle = "Teams ordered from flattest to most peaked distribution",
    x = "Player Touchiness Rank (1 = Most Involved)",
    y = "Team"
  ) +
  theme_minimal()

############################ Player Concentration | Social Network Strength to Final Standings ############################

# Merge flatness, player touchiness, and season rank into player data
player_touchiness_rank <- player_ridgeplot_counts %>%
  mutate(Team = as.character(Team)) %>%
  left_join(
    FinalStandings %>%
      mutate(TeamID = as.character(TeamID)) %>%
      select(TeamID, Rank),
    by = c("Team" = "TeamID")
  )

player_touchiness_rank <- player_touchiness_rank %>%
  mutate(
    Team = factor(Team),
    Team = fct_reorder(Team, Rank, .desc = FALSE)  # Rank 1 at top/front
  )

#filter to only top 18 players of touchiness... tails too long
player_touchiness_rank_top <- player_touchiness_rank %>%
  filter(TouchiestRank <= 18)

# Ridge plot (non-stacked), teams ordered by final season standings
TouchiestPlayers_Rank <- ggplot(player_touchiness_rank_top, aes(x = TouchiestRank, y = Team, height = TouchCount, group = Team)) +
  geom_density_ridges(stat = "identity", scale = 1.5, fill = "steelblue", alpha = 0.7) +
  labs(
    title = "Distribution of Player Touch Involvement by Team",
    subtitle = "Teams ordered by final season standings (Bottom of y-axis is 1st ranked team)",
    x = "Player Touchiness Rank (1 = Most Involved)",
    y = "Team"
  ) +
  theme_minimal() +
  theme(
    panel.grid.major.y = element_blank(),
    axis.text.y = element_text(size = 8),
    plot.title = element_text(face = "bold")
  )

#plot team flatness SD to final season rank in a simple scatter plot
#low standard deviation = flatter distribution (single players do not dominate touch interactions)
team_SD_rank <- team_SD %>%
  mutate(Team = as.character(Team)) %>%
  left_join(FinalStandings %>% select(TeamID, Rank), by = c("Team" = "TeamID"))

team_cv <- player_touchiness_rank_top %>%
  mutate(Team = as.character(Team)) %>%
  group_by(Team) %>%
  summarise(
    MeanTouches = mean(TouchCount),
    SDTouches = sd(TouchCount),
    CV = SDTouches / MeanTouches,
    .groups = "drop"
  )

team_cv_rank <- team_cv %>%
  left_join(FinalStandings %>% select(TeamID, Rank), by = c("Team" = "TeamID"))

#Look at CV (Coefficient of Variation): CV = SD / Mean -- normalized level of spread
# Plot scatter
CV_TouchConcentraion_Rank <- ggplot(team_cv_rank, aes(x = Rank, y = CV)) +
  geom_point(size = 3, color = "darkred") +
  geom_smooth(method = "lm", se = FALSE, color = "black", linetype = "dashed") +
  scale_x_reverse(breaks = 1:max(team_SD_rank$Rank)) +  # Lower rank = better
  labs(
    title = "Touch Concentration vs Final Season Rank",
    subtitle = "Higher SD = touches concentrated in fewer players",
    x = "Final Season Rank (1 = Best)",
    y = "Touch Count Standard Deviation (Per Team)"
  ) +
  theme_minimal()

CV_Stats <- cor.test(team_cv_rank$CV, team_cv_rank$Rank)

######Gini Coefficient################
team_gini <- player_touchiness_rank %>%
  group_by(Team) %>%
  summarise(
    Gini = Gini(TouchCount),
    .groups = "drop"
  )
team_gini_rank <- team_gini %>%
  mutate(Team = as.character(Team)) %>% 
  left_join(FinalStandings %>% select(TeamID, Rank), by = c("Team" = "TeamID"))

GiniPlot <- ggplot(team_gini_rank, aes(x = Rank, y = Gini)) +
  geom_point(size = 3, color = "darkgreen") +
  geom_smooth(method = "lm", se = FALSE, color = "black", linetype = "dashed") +
  scale_x_reverse(breaks = 1:max(team_gini_rank$Rank)) +  # Rank 1 = best, so reverse axis
  labs(
    title = "Gini Coefficient: Touch Inequality vs Final Season Rank",
    subtitle = "Higher Gini = More touches concentrated in fewer players",
    x = "Final Season Rank (1 = Best)",
    y = "Gini Coefficient of Touch Distribution"
  ) +
  theme_minimal()

GiniSum <- summary(lm(Gini ~ Rank, data = team_gini_rank))


#Percentage of touches from top 3 touchiest players
# Step 1: Sum total touches per team
team_total_touches <- player_touchiness_rank %>%
  group_by(Team) %>%
  summarise(TotalTouches = sum(TouchCount), .groups = "drop")

# Step 2: Get top 3 players per team and their touch count
top3_touches <- player_touchiness_rank %>%
  group_by(Team) %>%
  arrange(desc(TouchCount)) %>%
  slice_head(n = 3) %>%  # top 3 players
  summarise(Top3Touches = sum(TouchCount), .groups = "drop")

# Step 3: Merge and calculate proportion
touch_concentration <- top3_touches %>%
  left_join(team_total_touches, by = "Team") %>%
  mutate(Top3_Proportion = Top3Touches / TotalTouches)

# Step 4: Join with final standings to analyze relationship
touch_concentration <- touch_concentration %>%
  mutate(Team = as.character(Team)) %>%
  left_join(FinalStandings %>% select(TeamID, Rank), by = c("Team" = "TeamID"))

Concentration_top3 <- ggplot(touch_concentration, aes(x = Rank, y = Top3_Proportion)) +
  geom_point(size = 3, color = "darkblue") +
  geom_smooth(method = "lm", se = FALSE, color = "black", linetype = "dashed") +
  scale_x_reverse(breaks = 1:max(touch_concentration$Rank)) +
  labs(
    title = "Touch Concentration in Top 3 Players vs Final Season Rank",
    subtitle = "Higher values = more concentrated touch behavior in fewer players",
    x = "Final Season Rank (1 = Best)",
    y = "Proportion of Team Touches by Top 3 Players"
  ) +
  theme_minimal()

Concentration_top3_Stats <- cor.test(touch_concentration$Top3_Proportion, touch_concentration$Rank)

Concentration_top3_Sum <- summary(lm(Top3_Proportion ~ Rank, data = touch_concentration))

Output for Hypothesis 4

## 
## Call:
## lm(formula = Rank ~ Reciprocal_To_NonRecip_Ratio, data = Reciprocal_vs_Rank)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.8756 -2.5819  0.0691  2.4197  4.3007 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                    23.517      5.341   4.403  0.00086 ***
## Reciprocal_To_NonRecip_Ratio  -18.308      6.022  -3.040  0.01027 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.273 on 12 degrees of freedom
## Multiple R-squared:  0.4351, Adjusted R-squared:  0.388 
## F-statistic: 9.242 on 1 and 12 DF,  p-value: 0.01027

## 
##  Pearson's product-moment correlation
## 
## data:  team_cv_rank$CV and team_cv_rank$Rank
## t = -0.88655, df = 12, p-value = 0.3927
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6880078  0.3254580
## sample estimates:
##        cor 
## -0.2479353

## 
##  Pearson's product-moment correlation
## 
## data:  touch_concentration$Top3_Proportion and touch_concentration$Rank
## t = -1.4207, df = 12, p-value = 0.1809
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.7575206  0.1892233
## sample estimates:
##        cor 
## -0.3794525

Inter-Rater Reliability: ICC 

#Inter-Rater Analysis

#Goal is to determine how "similar" raters were
#We have a total of 12 matches that all raters watched

library(tidyverse)
library(data.table)
library(broom)
library(janitor)
library(readxl)
library(rmarkdown)
library(readr)
library(dplyr)
library(irr)
## Loading required package: lpSolve
library(fuzzyjoin)
## Warning: package 'fuzzyjoin' was built under R version 4.4.3
library(knitr)
## Warning: package 'knitr' was built under R version 4.4.3
source("Data_Management.R") #Runs and brings in Matches_final from Data_Management.R script
## Rows: 5877 Columns: 17
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (17): TouchID, SeasonMatchNumber, Time, Team, PlayersInvolved, FieldLoca...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
## Rows: 5562 Columns: 17
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (17): TouchID, SeasonMatchNumber, Time, Team, PlayersInvolved, FieldLoca...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
## Rows: 5559 Columns: 17
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (17): TouchID, SeasonMatchNumber, Time, Team, PlayersInvolved, FieldLoca...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
## Rows: 141 Columns: 52
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (52): MatchID, SeasonMatchNumber, TeamName, Date_of_Match, Opponent, Hom...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
## New names:
## Rows: 137 Columns: 53
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (53): MatchID, SeasonMatchNumber, TeamName, Date_of_Match, Opponent, Hom...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
## Rows: 137 Columns: 52
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (52): MatchID, SeasonMatchNumber, TeamName, Date_of_Match, Opponent, Hom...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
## Rows: 14 Columns: 3
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (3): Team Name 2024 Season, TeamID, New Name 2025
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
## Rows: 14 Columns: 28
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (1): Team
## dbl (27): TeamID, Week1, Week2, Week3, Week4, Week5, Week6, Week7, Week8, We...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
## Rows: 14 Columns: 11
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (4): Team, SeasonWLD, HomeWLD, AwayWLD
## dbl (7): Rank, TeamID, Points, MatchesPlayes, SeasonGoalsFor, SeasonGoalsAga...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
## New names:
## New names:
#Dataframe "Touches_interrater" contains all the touches recorded for this analysis

# Should I exclude
# Situations excluded from core analysis for these hypotheses: Goals For/Against, Substitutions
Exclude_Touch <- c("TA", "CO", "NEG")
Exclude_Situation <- c("GF", "GA", "SUB")

Interrater <- Touches_interrater %>%  #duplicate and filter
  filter(!(HapticRitual %in% Exclude_Touch)) %>%
  filter(!(Situation %in% Exclude_Situation))

############################ Simple Frequency Check ############################

#Count check per match (simply how many each rater saw)

touch_counts <- Interrater %>%
  group_by(SeasonMatchNumber, Rater) %>%
  summarise(TouchCount = n(), .groups = "drop")

# Plot frequency per match per rater
interrater_plot <- ggplot(touch_counts, aes(x = factor(SeasonMatchNumber), y = TouchCount, fill = Rater)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(title = "Touch Count per Match by Rater",
       x = "Season Match Number",
       y = "Touch Count") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

###ICC - Intraclass Correlation Coefficient - Interval data:

# reshape your data: rows = matches, columns = raters
icc_data <- Interrater %>%
  group_by(SeasonMatchNumber, Rater) %>%
  summarise(Count = n(), .groups = "drop") %>%
  pivot_wider(names_from = Rater, values_from = Count)

# Apply ICC (two-way random effects model)
icc_result <- icc(icc_data[,-1], model = "twoway", type = "agreement", unit = "single")
interrater_plot

icc_result
##  Single Score Intraclass Correlation
## 
##    Model: twoway 
##    Type : agreement 
## 
##    Subjects = 12 
##      Raters = 3 
##    ICC(A,1) = 0.788
## 
##  F-Test, H0: r0 = 0 ; H1: r0 > 0 
##  F(11,23.9) = 11.9 , p = 3.33e-07 
## 
##  95%-Confidence Interval for ICC Population Values:
##   0.551 < ICC < 0.926

Data/Sample Sizes

Quick Summary of Data/Sample Sizes:

Note the filtered touch count is what was mostly used in the above analysis. The cut from about 14000 touch instances to 7000 instances is due to excluding substitutes, goal celebrations, and situations such as collisions which were not defined as pro-social touches.

# Data Summary and Overview
# Gives Simple overall counts, tables, data make-up etc

library(tidyverse)
library(data.table)
library(broom)
library(janitor)
library(readxl)
library(rmarkdown)
library(readr)
library (dplyr)


############################ Complete data summary | No filtering ############################ 

#Create Tables that summarizes complete data of "Touches_final" and "Matches_final"

Touches_Summary <- Touches_final
Matches_Summary <- Matches_final

Total_Touch_Instance_count <- nrow(Touches_Summary) #count total number of touches recorded

Total_Match_Count <- n_distinct(Touches_Summary$SeasonMatchNumber) #total number of matches watched

Total_Teams <- n_distinct(Touches_Summary$Team) #teams recorded

Total_Matches_perTeam <- 26 #Matches each team played (verified below)

Summary_Table_A <- tibble(
  Variable = c("Total_Touch_Instance_count", "Total_Match_Count", "Total_Teams", "Total_Matches_perTeam"),
  Value = c(
    nrow(Touches_Summary),
    n_distinct(Touches_Summary$SeasonMatchNumber),
    n_distinct(Touches_Summary$Team),
    26  # Manually verified
  )
)

Matches_Summary <- Matches_Summary %>%
  mutate(TeamName = case_when(
    TeamName %in% c("Racing Louisville", "Racing louisville FC", "Louisville Racing") ~ "Racing Louisville FC",
    TeamName %in% c("NC Courage", "Carolina Courage") ~ "North Carolina Courage",
    TeamName %in% c("KC Current") ~ "Kansas City Current",
    TeamName %in% c("Chicago Redstar FC") ~ "Chicago Red Stars",
    TeamName %in% c("Portland Thorns") ~ "Portland Thorns FC",
    TeamName %in% c("Gotham FC") ~ "NJ/NY Gotham FC",
    TeamName %in% c("San Diego Wave") ~ "San Diego Wave FC",
    TeamName %in% c("Seattle Reign") ~ "Seattle Reign FC",
    TRUE ~ TeamName
  ))

TeamMatchCounts <- Matches_Summary %>%
  count(TeamName, name = "MatchesPlayed")

TeamMatchCounts <- TeamMatchCounts %>%
  left_join(Team_IDs, 
            by = c("TeamName" = "Team Name 2024 Season"))

ByTeam_Total_Touch_Instance_count <- Touches_Summary %>% 
  count(Team, name = "Total Season Touches") %>% 
  rename(TeamID = Team)

TeamMatchCounts <- TeamMatchCounts %>%
  left_join(ByTeam_Total_Touch_Instance_count, 
            by = c("TeamID" = "TeamID"))

############################ Core Hyp data summary | Includes filtering ############################ 

Filtered_Touch_Summary <- Touches_CoreHyp

Filtered_Touch_Instance_count <- nrow(Filtered_Touch_Summary)

#Count of frequency of touches per team
Filtered_Touches_by_team <- Touches_by_team

Filtered_TeamMatchCounts <- TeamMatchCounts %>%
  left_join(Filtered_Touches_by_team, 
            by = c("TeamID" = "Team"))

Summary_Table_B <- tibble(
  Variable = c("Total_Touch_Instance_count", "Filtered_Touch_Instance_count", "Total_Match_Count", "Total_Teams", "Total_Matches_perTeam"),
  Value = c(
    Total_Touch_Instance_count,
    Filtered_Touch_Instance_count,
    Total_Match_Count,
    Total_Teams,
    Total_Matches_perTeam
  )
)

Summary_Table_B
## # A tibble: 5 × 2
##   Variable                      Value
##   <chr>                         <dbl>
## 1 Total_Touch_Instance_count    14869
## 2 Filtered_Touch_Instance_count  7955
## 3 Total_Match_Count               182
## 4 Total_Teams                      14
## 5 Total_Matches_perTeam            26